Anti-government protesters in Tahrir Square shout in anger after the speech by Egyptian president Hosni Mubarak. Photograph: Chris Hondros/Getty Images

The victory celebrations in Tahrir Square had been going on for hours when the moment arrived for what almost everyone assumed would be Hosni Mubarak's resignation speech, but the Egyptian president was determined to tease them a little longer.

On state TV, the news bulletin came and went, with no sign of the president. Then came the weather forecast. Then a promotional film showing what a wonderful place Egypt is and then, rather surprisingly, a discussion about high-level corruption.

Finally, the man who has presided over high-level corruption for the last 30 years appeared – about 40 minutes late. By that stage, anyone tuned to Alarabiya – the Saudi TV channel set up as a rival to al-Jazeera – already knew what he was going to say. Someone had leaked the speech to them.

And what a speech. By the standards of any modern politician, it was truly dreadful: in turns vain, arrogant, patronising, condescending and defiant. Above all, it showed Mubarak totally out of touch with the mood of the country and the will of the people that he governs. The only thing to be said in its favour is that it illustrated, in just a few hundred words, all the reasons why he ought to go (even if he's still refusing to do so).

He began by addressing the people as his "sons and daughters" – a phrase that might slip past unnoticed, though in fact it encapsulates the fundamental problem with Arab leaders and how they perceive themselves and their citizens. They behave like the traditional head of an Arab household, the paterfamilias – a remote, supposedly wise and almost God-like figure who rarely speaks but, when he does, must always be obeyed because he knows what's best for his children.

By the time he got to "I am determined to live up to my promises" a few sentences further on, it was clear he had no intention of resigning – and he followed this up with a series of "commitments" which, on past form, cannot be taken at face value.

He even appeared to backtrack on Egypt's much criticised and semi-permanent "emergency" law, saying it would be lifted only when "calm and stability" return and conditions are "suitable". Just a few months ago, the regime had been promising that the 43-year "emergency" would end as soon as the draft of its new anti-terrorism law had been finalised.

Before long, though, the speech was drifting off into familiar blather about Mubarak's service to the country and his military achievements:

"I was as young as Egypt's youth today, when I learned the Egyptian military honour, allegiance and sacrifice for my country.
I have spent a lifetime defending its soil and sovereignty. I witnessed its wars, with its defeats and victories …
It was the happiest day of my life when I raised the flag of Egypt over Sinai."

In Tahrir, the cheers turned to jeers and chants of "Mubarak out!" resumed. By the end, people were taking off their shoes and waving them at the TV screens – the ultimate Arab insult.

What are we to make of these extraordinary events, and what do they herald for today? One theory among Egyptians is that the speech was intentionally provocative, calculated to arouse the ire of the protesters, goading them into violence – and thus providing a pretext for martial law. That may be a bit too conspiratorial.

What exactly does that mean, and how does it relate to Mubarak's non-resignation speech? Indeed, why did Mubarak need to make a speech at all if he is not resigning?

According to reports, the supreme council has met only three times in its history: in 1967 and 1973 (when the country was at war) – and on Thursday. Thursday's meeting was held without its chairman, Mubarak, and apparently the meeting was adjourned without formally concluding. A second communique has failed to clarify the army's position.

Possibly, as one Egyptian commentator suggested on the BBC, the army was attempting a coup which Mubarak had fended off by threatening to unleash his Republican Guard upon them.

Whatever the truth in that, when the head of the ruling party says it's time for the president to step aside, when the government media seem increasingly uncertain about the message they are supposed to be conveying and three former ministers have been forbidden to leave the country pending possibly corruption charges, the inescapable conclusion is that the struggle on the streets is no longer the only game in town – and that key members of the regime are now fighting amongst themselves.